# Homework Help: Find the ratio of the frequency of the damped oscillator

1. Oct 1, 2007

### kreil

1. The problem statement, all variables and given/known data
Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.

2. Relevant equations
$$T=\frac{ 2\pi}{w_1}$$

$$w_1^2=w_0^2- {\Beta}^2$$

3. The attempt at a solution
I know the answer is $$\frac{w_1}{w_0}=\frac{8 {\pi}}{\sqrt{64 {\pi}^2+1}}$$

However, I think I am missing an equation here because using only the two above i cannot obtain this answer. If someone could point me in the right direction I would appreciate it!

Josh

Last edited: Oct 1, 2007
2. Oct 1, 2007

### cristo

Staff Emeritus
Well, firstly you should explain your symbols. I presume you are using w to mean omega; the frequency of the oscillator. What is the definition of the natural frequency?